To determine which equations can be rearranged to solve for the frequency of a wave, let's analyze each equation step by step:
1. wavelength = frequency / speed
We need to solve for frequency:
[tex]\[
\text{wavelength} = \frac{\text{frequency}}{\text{speed}}
\][/tex]
Multiply both sides by speed:
[tex]\[
\text{wavelength} \times \text{speed} = \text{frequency}
\][/tex]
Therefore, this equation can be rearranged to calculate the frequency:
[tex]\[
\text{frequency} = \text{wavelength} \times \text{speed}
\][/tex]
2. frequency = wavelength / speed
This equation is already solved for frequency, so no rearrangement is needed.
3. wavelength = speed / frequency
We need to solve for frequency:
[tex]\[
\text{wavelength} = \frac{\text{speed}}{\text{frequency}}
\][/tex]
Multiply both sides by frequency:
[tex]\[
\text{wavelength} \times \text{frequency} = \text{speed}
\][/tex]
Divide both sides by wavelength:
[tex]\[
\text{frequency} = \frac{\text{speed}}{\text{wavelength}}
\][/tex]
Therefore, this equation can be rearranged to calculate the frequency:
[tex]\[
\text{frequency} = \frac{\text{speed}}{\text{wavelength}}
\][/tex]
4. frequency = speed x wavelength
This equation is already solved for frequency, so no rearrangement is needed.
Given the analysis, the equations that can be rearranged to calculate the frequency of a wave are:
1. wavelength = frequency / speed
3. wavelength = speed / frequency
Thus, the correct equations that could be rearranged to calculate the frequency are given by the indices: [tex]\([1, 3]\)[/tex].
